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If x^{n+1} - 2x^n=3x^n, then what is the value of x^n?

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Bunuel
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If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   17 Jul 2016, 11:25
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If \(x^{n+1} - 2x^n=3x^n\), then what is the value of x^n?

(1) \(x^{n+1}=625\)

(2) x=5
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A
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   17 Jul 2016, 12:04
Bunuel wrote:
If \(x^{n+1} - 2x^n=3x^n\), then what is the value of x?

(1) \(x^{n+1}=625\)

(2) x=5

Hi Bunuel , do we need to solve for the value of n ?

\(x^{n+1} - 2x^n=3x^n\)
\(x^{n+1} = 2x^n + 3x^n = x^n (2+3) = 5 * x^n\)
=> x = 5

(1) \(x^{n+1}=625 = 5^4\)
We can solve for the value of n
Sufficient

(2) x=5
Not sufficient as we already know x

Answer A
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Bunuel
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   17 Jul 2016, 12:08
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Skywalker18 wrote:
Bunuel wrote:
If \(x^{n+1} - 2x^n=3x^n\), then what is the value of x?

(1) \(x^{n+1}=625\)

(2) x=5

Hi Bunuel , do we need to solve for the value of n ?

\(x^{n+1} - 2x^n=3x^n\)
\(x^{n+1} = 2x^n + 3x^n = x^n (2+3) = 5 * x^n\)
=> x = 5

(1) \(x^{n+1}=625 = 5^4\)
We can solve for the value of n
Sufficient

(2) x=5
Not sufficient as we already know x

Answer A


We need to find the value of x^n. Edited. Thank you.
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   17 Jul 2016, 12:55
from given equation x=5.
now statement 1. x^(n+1)=625. can be solved for n and then x^n. so sufficient.

statement 2- already given in the stem. so not sufficient.

ANS A.
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   18 Jul 2016, 05:39
STEM: x^(n+1) - 2x^n=3x^n
or, x^n.x=5x^n
or, x=5...........(i)
x^n=?

STAT-1:x^(n+1)=625
or, 5^(n+1)=5^4
or, n+1=4
or, n=3.........sufficient

STAT-2: x=5, already given at STEM..... insufficient

ANS:A
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If x^n+1 - 2x^n = 3x^n, then what is the value of x^n? [#permalink] New post   18 Jul 2016, 08:12
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If \(x^{n+1} - 2x^n = 3x^n\), then what is the value of \(x^n\)?

Statement #1: \(x^{n+1} = 625\)

Statement #2: \(x = 5\)

One of the statements of this DS problem is a tautological statement. To find that a statement is tautological implies more than if we merely find that the statement is insufficient. For a discussion of this subtle logical issue, as well as the OE for this particular question, see:
GMAT Data Sufficiency Logic: Tautological Statements

Mike :-)
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   19 Jul 2016, 06:34
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Bunuel wrote:
If \(x^{n+1} - 2x^n=3x^n\), then what is the value of x^n?

(1) \(x^{n+1}=625\)

(2) x=5


Answer should be C.

Statement 1 : x^n+1=625. We could have either 5^4=625 => x=5

or (-5)^4=625 => x=-5.

=> x^n could be either 125 or -125 -- Insufficient.

Statement 2: x=5. But we don't know the value of n.--> Insufficient.

Combining both the statements, we know x=5 and n=3 => x^n=125.

hence, answer is C
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   19 Jul 2016, 07:12
Bunuel wrote:
If \(x^{n+1} - 2x^n=3x^n\), then what is the value of x^n?

(1) \(x^{n+1}=625\)

(2) x=5


Statement 1 First of all we will solve the equation

x^(n+1)=625 then 5^(3+1) so x = 5 or x = -5 Clearly Insufficient

Statement 2 x=5 that doesn't really say anything so clearly insufficient

Combining both of them we get x=5 and n =3 so answer is C
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   24 Jan 2017, 07:14
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\(x^{n+1}−2x^n=3x^n\)
\(x^{n+1} = 5x^n\) .... eq (1)

From this expression, we cannot say that \(x=5\) as \(x\) can be 0 too.

1) \(x^{n+1} = 625\)

From this expression, we come to know that x is not equal to 0. Therefore, we can divide both the sides of eq (1) by \(x^n\).
Thus, we get \(x=5\) and therefore \(n=3\). Sufficient.

2) x=5

With this information in hand, we cannot get a definitive value for \(n\). Insufficient.
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink] New post   18 Apr 2023, 12:06
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Re: If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? [#permalink]
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